For Mr Bush, the imminence of his departure from the White House in just six days is likely, if anything, to add urgency to plans to penalise President Saddam for his violations of the United Nations ceasefire resolutions imposed on his nation after the conclusion of the 1991 Gulf conflict.
If there is a chance to inflict punishment on the Iraqi leader swiftly, Mr Bush will be anxious to do that before he becomes a private citizen again.
The precise nature of the military strike against Iraq - in particular, which targets the allies want to hit - remained until the last moment a closely guarded secret. But if somewhere within the strategy lies a perceived chance finally to topple President Saddam, then the desire to act quickly will be all the stronger.
Mr Bush, whose victory in the Gulf war has been marred by the continuing presence of President Saddam in Baghdad, could wish nothing more than to rid the Middle East of the dictator, as his final legacy as US president.
What is equally clear, however, is the determination of Mr Clinton to leave no daylight between himself and his predecessor on policy towards President Saddam. There was some expectation yesterday that Mr Bush and Mr Clinton would issue a statement jointly on the launching of a new assault on Iraq as a symbol of the continuity of policy between them.
The point was again underlined yesterday by Mr Clinton's designated secretary of state, Warren Christopher, who was in Washington attending his appointment hearings in the Senate. 'I say with great determination that Saddam Hussein should not doubt for a second that we, the incoming administration, will meet the test,' Mr Christopher told the Senate panel.
Adopting the kind of language long used by the Bush White House towards Iraq, Mr Christopher went on: 'We will insist upon the unconditional compliance with the UN resolutions. We repeatedly made it clear that we stand shoulder-to-shoulder with the current administration in our determination to make sure that Saddam Hussein does not miscalculate America's resolve again.'
It is significant also that another leading figure in the Clinton team, Les Aspin, designated as defense secretary, distinguished himself from some of his Democratic colleagues in Congress two years ago by strongly supporting the initial Desert Storm operation to oust President Saddam from Kuwait. He has reiterated his position that US force should be used to deter aggression by dictators such as the Iraqi leader.
On the assumption that the two-and-a-half year confrontation with Iraq cannot be resolved in six short days, it has long been plain that president-elect Clinton's campaign pledge to focus 'like a laser beam' on domestic policy at the expense of world affairs will be knocked aside by the Iraqi crisis.
All the signs suggest that Iraq, and perhaps the continuing crises in Bosnia and Somalia, will be occupying him, perhaps from the very moment of his taking the oath of office next Wednesday.